Cut points and canonical splittings of hyperbolic groups

  title={Cut points and canonical splittings of hyperbolic groups},
  author={Brian H. Bowditch},
  journal={Acta Mathematica},
  • B. Bowditch
  • Published 1 September 1998
  • Mathematics
  • Acta Mathematica
In this paper, we give a construction of the JSJ splitting of a one-ended hyperbolic group (in the sense of Gromov [Gr]), using the local cut point structure of the boundary. In particular, this gives the quasiisometry invariance of the splitting, as well the annulus theorem for hyperbolic groups. The canonical nature of the splitting is also immediate from this approach. The notion of a JSJ splitting, in this context, was introduced by Sela [Se], who constructed such splittings for all… 

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